I am running this code and oddly, nothing happens. There is no error nor does it freeze. It simply just runs the code without storing variables, nothing is printed out and it doesn't open the window that is supposed to show the plot. So it simply does nothing. It is very odd. This worked only a few minutes ago and I did not change anything about it previously. I did make sure that the variable explorer is displaying all the definitions in the script. I intentionally removed the plotting section at the end since it just made the code set longer and the same issue persists here without it.
Code:
#Import libraries
import numpy as np
from scipy.integrate import odeint
#from scipy.integrate import solve_ivp
from time import time
import matplotlib.pyplot as plt
from matplotlib.pyplot import grid
from mpl_toolkits.mplot3d import Axes3D
import numpy, scipy.io
from matplotlib.patches import Circle
'''
import sympy as sy
import random as rand
from scipy import interpolate
'''
'''
Initiate Timer
'''
TimeStart = time()
'''
#User defined inputs
'''
TStep = (17.8E-13)
TFinal = (17.8E-10)
R0 = 0.02
V0X = 1E7
ParticleCount = 1 #No. of particles to generate energies for energy generation
BInput = 0.64 #Magnitude of B field near pole of magnet in experiment
ScaleV0Z = 1
'''
#Defining constants based on user input and nature (Cleared of all errors!)
'''
#Defining Space and Particle Density based on Pressure PV = NkT
k = 1.38E-23 #Boltzman Constant
#Natural Constants
Q_e = -1.602E-19 #Charge of electron
M_e = 9.11E-31 #Mass of electron
JToEv = 6.24E+18 #Joules to eV conversion
EpNaut = 8.854187E-12
u0 = 1.256E-6
k = 1/(4*np.pi*EpNaut)
QeMe = Q_e/M_e
'''
Create zeros matrices to populate later (Cannot create TimeIndex array!)
'''
TimeSpan = np.linspace(0,TFinal,num=round((TFinal/TStep)))
TimeIndex = np.linspace(0,TimeSpan.size,num=TimeSpan.size)
ParticleTrajectoryMat = np.zeros([91,TimeSpan.size,6])
BFieldTracking = np.zeros([TimeSpan.size,3])
InputAngle = np.array([np.linspace(0,90,91)])
OutputAngle = np.zeros([InputAngle.size,1])
OutputRadial = np.zeros([InputAngle.size,1])
'''
Define B-Field
'''
def BField(x,y,z):
InputCoord = np.array([x,y,z])
VolMag = 3.218E-6 #Volume of magnet in experiment in m^3
BR = np.sqrt(InputCoord[0]**2 + InputCoord[1]**2 + InputCoord[2]**2)
MagMoment = np.array([0,0,(BInput*VolMag)/u0])
BDipole = (u0/(4*np.pi))*(((3*InputCoord*np.dot(MagMoment,InputCoord))/BR**5)-(MagMoment/BR**3))
#BVec = np.array([BDipole[0],BDipole[1],BDipole[2]])
#print(BDipole[0],BDipole[1],BDipole[2])
return (BDipole[0],BDipole[1],BDipole[2])
'''
Lorentz Force Differential Equations Definition
'''
def LorentzForce(PosVel,t,Constants):
X,Y,Z,VX,VY,VZ = PosVel
Bx,By,Bz,QeMe = Constants
BFInput = np.array([Bx,By,Bz])
VelInput = np.array([VX,VY,VZ])
Accel = QeMe * (np.cross(VelInput, BFInput))
LFEqs = np.concatenate((VelInput, Accel), axis = 0)
return LFEqs
'''
Cartesean to Spherical coordinates converter function. Returns: [Radius (m), Theta (rad), Phi (rad)]
'''
def Cart2Sphere(xIn,yIn,zIn):
P = np.sqrt(xIn**2 + yIn**2 + zIn**2)
if xIn == 0:
Theta = np.pi/2
else:
Theta = np.arctan(yIn/xIn)
Phi = np.arccos(zIn/np.sqrt(xIn**2 + yIn**2 + zIn**2))
SphereVector = np.array([P,Theta,Phi])
return SphereVector
'''
Main Loop
'''
for angletrack in range(0,InputAngle.size):
MirrorAngle = InputAngle[0,angletrack]
MirrorAngleRad = MirrorAngle*(np.pi/180)
V0Z = np.abs(V0X/np.sin(MirrorAngleRad))*np.sqrt(1-(np.sin(MirrorAngleRad))**2)
V0Z = V0Z*ScaleV0Z
#Define initial conditions
V0 = np.array([[V0X,0,V0Z]])
S0 = np.array([[0,R0,0]])
ParticleTrajectoryMat[0,:] = np.concatenate((S0,V0),axis=None)
for timeplace in range(0,TimeIndex.size-1):
ICs = np.concatenate((S0,V0),axis=None)
Bx,By,Bz = BField(S0[0,0],S0[0,1],S0[0,2])
BFieldTracking[timeplace,:] = np.array([Bx,By,Bz])
AllConstantInputs = [Bx,By,Bz,QeMe]
t = np.array([TimeSpan[timeplace],TimeSpan[timeplace+1]])
ODESolution = odeint(LorentzForce,ICs,t,args=(AllConstantInputs,))
ParticleTrajectoryMat[angletrack,timeplace+1,:] = ODESolution[1,:]
S0[0,0:3] = ODESolution[1,0:3]
V0[0,0:3] = ODESolution[1,3:6]
MatSize = np.array([ParticleTrajectoryMat.shape])
RowNum = MatSize[0,1]
SphereMat = np.zeros([RowNum,3])
SphereMatDeg = np.zeros([RowNum,3])
for cart2sphereplace in range(0,RowNum):
SphereMat[cart2sphereplace,:] = Cart2Sphere(ParticleTrajectoryMat[angletrack,cart2sphereplace,0],ParticleTrajectoryMat[angletrack,cart2sphereplace,1],ParticleTrajectoryMat[angletrack,cart2sphereplace,2])
for rad2deg in range(0,RowNum):
SphereMatDeg[rad2deg,:] = np.array([SphereMat[rad2deg,0],(180/np.pi)*SphereMat[rad2deg,1],(180/np.pi)*SphereMat[rad2deg,2]])
PhiDegVec = np.array([SphereMatDeg[:,2]])
RVec = np.array([SphereMatDeg[:,0]])
MinPhi = np.amin(PhiDegVec)
MinPhiLocationTuple = np.where(PhiDegVec == np.amin(PhiDegVec))
MinPhiLocation = int(MinPhiLocationTuple[1])
RAtMinPhi = RVec[0,MinPhiLocation]
OutputAngle[angletrack,0] = MinPhi
OutputRadial[angletrack,0] = RAtMinPhi
print('Mirror Angle Input (In deg): ',InputAngle[0,angletrack])
print('Mirror Angle Output (In deg): ',MinPhi)
print('R Value at minimum Phi (m): ',RAtMinPhi)
InputAngleTrans = np.matrix.transpose(InputAngle)
CompareMat = np.concatenate((InputAngleTrans,OutputAngle),axis=1)
Related
I've been having problems trying to estimate two variables while using fsolve. Below is the code
def f(variables):
#Ideal
n=0 #this is passed as an argument but given in this example for simplicity
P1 = 101325; T1 = 300
q = 'H2:2,O2:1,N2:{}'.format(molno[n])
mech = 'H2O2sandan.cti'
cj_speed,R2,plot_data = CJspeed(P1,T1,q,mech,fullOutput=True)
gas = PostShock_fr(cj_speed, P1, T1, q, mech)
Ta = gas.T; Ps = gas.P;
CVout1 = cvsolve(gas)
taua = CVout1['ind_time']
Tb = Ta*1.01
gas.TPX = Tb,Ps,q
CVout2 = cvsolve(gas)
taub = CVout2['ind_time']
#Constant Volume
k,Ea = variables
T_0_1= Tvn_mg_d[n]
T_vn_1 = Tvn_mg_d[n]
den = rhovn_mg_d[n]
t = np.linspace(0,0.0001,100000000)
qr = Q_mg[n]
perfect_var = T_vn_1,den,Ea,k,qr
sol_t= odeint(ode,T_0_1,t=t,args=(perfect_var,))
index = np.argmax(np.gradient(sol_t[:,0]))
tau_cv_1 = t[index]
T_0_2= Tvn_mg_d[n]*1.01
T_vn_2 = Tvn_mg_d[n]*1.01
den = rhovn_mg_d[n]
t = np.linspace(0,0.0001,100000000)
qr = Q_mg[n]
perfect_var = T_vn_2,den,Ea,k,qr
sol_t= odeint(ode,T_0_2,t=t,args=(perfect_var,))
index = np.argmax(np.gradient(sol_t[:,0]))
tau_cv_2 = t[index]
root1 = taua - t_cv_1
root2 = taub - t_cv_2
return[root1,root2]
import scipy.optimize as opt
k_guess = 95000
Ea_guess = 28*300
solution = opt.fsolve(f,(k_guess,Ea_guess))
print(solution)
I want to find values of k_guess and Ea_guess such that roo1 and roo2 are 0 (i.e. taua = t_cv_1 and taub = t_cv_2). However I don't know if I've used fsolve the right way as the values returned seem to be way off. Am I returning the right thing? I also get the below error:
lsoda-- warning..internal t (=r1) and h (=r2) are
such that in the machine, t + h = t on the next step
(h = step size). solver will continue anyway
What am I doing wrong here?
I am testing some equations of motion with odeint. I am trying to integrate and test these while saying my control (us) is 0 the whole time. However, I get the above-mentioned error, and I do not understand why. Any advice is much appreciated!
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint
from scipy.interpolate import interp1d
import pickle
Ro = 6371000 #m
hs = -7254.24 #m scale height
rhosl = 1.225 #kg^3
Aref = 250 #m^2
m = 92079 #kg mass of vehicle
#cl and cd spline
dat = pickle.load(open('clp.pkl','rb'))
AOA =dat[0]
cl = dat[1]
cd = dat[2]
AOAnew = AOA.tolist()
cl1 = cl.tolist()
cd1 = cd.tolist()
clnew = interp1d(AOAnew,cl1,kind='linear')
cdnew = interp1d(AOAnew,cd1,kind='linear')
def rhos(h):
rho = rhosl*np.exp((hs)/h)
return rho
def f(t,xs):
r,theta,phi,V,gamma,psi = xs
L = Ro*(rhos(r))*V**2*Aref*(clnew(gamma))/(2*m)
D = Ro*(rhos(r))*V**2*Aref*(cdnew(gamma))/(2*m)
us = 0
drdot = V*np.sin(gamma)
dthetadot = (V*np.cos(gamma)*np.sin(gamma))/(r*np.cos(phi))
dphidot = (V*np.cos(gamma)*np.cos(psi))/r
dVdot = -D - np.sin(gamma/r**2)
dgammadot = (L*np.cos(us)/V) + (V**2 - (1/r))*np.cos(gamma/(V*r))
dpsidot = L*np.sin(us)/(V*np.cos(gamma)) + V*np.cos(gamma)*np.sin(psi)*np.tan(phi/r)
return [drdot,dthetadot,dphidot,dVdot,dgammadot,dpsidot]
#initial/terminal conditiions
h0 = 79248
theta0 = 0
phi0 = 0
V0 = 7802.88
gamma0 = -1/np.pi
psi0 = 90/np.pi
y0 = [h0,theta0,phi0,V0,gamma0,psi0]
t = np.linspace(0,20)
y = odeint(f,y0,t)
plt.plot(t,y)
plt.show()
You need to pass tfirst=True to odeint, as it expects f(y, t) by default.
i have writing this code but in my code there is error, how can i make spiral arms from this code by used profile used below i want to create surface density profile using spiral arms of the galaxy
import numpy as np
import matplotlib.pyplot as plt
from math import*
#r,theta = meshgrid(np.arange(0,200,1), np.arange(0,360,1))
t = 1
c = 100
alpha = 12 #degree
m = 2
rd = 5
sigd = 35
omegap = 8.4
r,theta = np.meshgrid(np.arange(1,200,1), np.arange(1,360,1))
def k(m,r):
k1 = (m/r)*(1/0.212)
#print(k1)
return k1
def sig0(sigd,r,rd):
sig_0 = sigd*np.exp(-r/rd)
return sig_0
def phi (m,r):
phi_1 = m*(1/0.212)*np.log(r)
return phi_1
def omega (r):
omega_1 = (200/r)+1.37
return omega_1
def kappa (r):
kppa= (400*sqrt(0.5))/r
return kppa
def xt(c,m,r):
x_t = ((k(m,r)**2)*(c**2))/((kappa(r))**2)
return x_t
def v(m,omegap,r):
v_1 = (m/kappa(r))*(omegap-omega(r))
return v_1
def del_12 (c,r,m,omegap):
de1 = (1-((4*xt(c,m,r))*((1-v(m,omegap,r)**2))))**(1/2)
return de1
def sig(r,m,t,theta,c,sigd,rd,omegap):
r,theta = np.meshgrid(np.arange(1,200,1), np.arange(1,360,1))
sig1 = sig0(sigd,r,rd)+(((abs(k(m,r)))/r**(1/2))*(1/(abs(del_12(c,m,r,omegap))**(1/2)))*(np.cos(omegap*m*t-m*theta+phi(m,r))))
#+ ((abs(k(m,r)))/r**(1/2))*(1/abs(del_12(c,r,m,omegap))**(1/2))*np.cos(omegap*m*t-m*theta+phi)
return sig1
model = sig(r,m,t,theta,c,sigd,rd,omegap)
print(model)
fig=plt.figure()
ax1=fig.add_subplot(121)
ax1.imshow(model)
#plt.contour(x,y,galaxy_model_1)
#pf.writeto('gal_1.fits', galaxy_model_1, clobber=1)
#ax2=fig.add_subplot(122, axisbg='white')
#ax2.imshow((abs(galaxy_model_2))**0.2)
plt.show()
more information about this code is given by this reference
Contribution of spiral arms to the surface brightness distribution
of disk galaxies
http://articles.adsabs.harvard.edu/pdf/1997A%26A...318..741S
There is my code. I fixed it like this:
# Take 3 digits for significant figures in this code
import numpy as np
from math import *
from astropy.constants import *
import matplotlib.pyplot as plt
import time
start_time = time.time()
"""
G = Gravitational constant
g0 = Standard acceleration of gravity ( 9.8 m/s2)
M_sun = Solar mass
M_earth = Earth mass
R_sun = Solar darius
R_earth = Earth equatorial radius
au = Astronomical unit
Astropy.constants doesn't have any parameter of moon.
So I bring the data from wikipedia(https://en.wikipedia.org/wiki/Moon)
"""
M_moon = 7.342E22
R_moon = 1.737E6
M_earth = M_earth.value
R_earth = R_earth.value
G = G.value
perigee, apogee = 3.626E8, 4.054E8
position_E = np.array([0,0])
position_M = np.array([(perigee+apogee)/2.,0])
position_com = (M_earth*position_E+M_moon*position_M)/(M_earth+M_moon)
rel_pE = position_E - position_com
rel_pM = position_M - position_com
F = G*M_moon*M_earth/(position_M[0]**2)
p_E = {"x":rel_pE[0], "y":rel_pE[1],"v_x":0, "v_y":(float(F*rel_pE[0])/M_earth)**.5}
p_M = {"x":rel_pM[0], "y":rel_pM[1],"v_x":0, "v_y":(float(F*rel_pM[0])/M_moon)**.5}
print(p_E, p_M)
t = range(0,365)
data_E , data_M = [], []
def s(initial_velocity, acceleration, time):
result = initial_velocity*time + 0.5*acceleration*time**2
return result
def v(initial_velocity, acceleration, time):
result = initial_velocity + acceleration*time
return result
dist = float(sqrt((p_E["x"]-p_M['x'])**2 + (p_E["y"]-p_M["y"])**2))
xE=[]
yE=[]
xM=[]
yM=[]
data_E, data_M = [None]*len(t), [None]*len(t)
for i in range(1,366):
data_E[i-1] = p_E
data_M[i-1] = p_M
dist = ((p_E["x"]-p_M["x"])**2 + (p_E["y"]-p_M["y"])**2)**0.5
Fg = G*M_moon*M_earth/(dist**2)
theta_E = np.arctan(p_E["y"]/p_E["x"])
theta_M = theta_E + np.pi #np.arctan(data_M[i-1]["y"]/data_M[i-1]["x"])
Fx_E = Fg*np.cos(theta_E)
Fy_E = Fg*np.sin(theta_E)
Fx_M = Fg*np.cos(theta_M)
Fy_M = Fg*np.sin(theta_M)
a_E = Fg/M_earth
a_M = Fg/M_moon
v_E = (p_E["v_x"]**2+p_E["v_y"]**2)**.5
v_M = (p_M["v_x"]**2+p_M["v_y"]**2)**.5
p_E["v_x"] = v(p_E["v_x"], Fx_E/M_earth, 24*3600)
p_E["v_y"] = v(p_E["v_y"], Fy_E/M_earth, 24*3600)
p_E["x"] += s(p_E['v_x'], Fx_E/M_earth, 24*3600)
p_E["y"] += s(p_E['v_y'], Fy_E/M_earth, 24*3600)
p_M["v_x"] = v(p_M["v_x"], Fx_M/M_moon, 24*3600)
p_M["v_y"] = v(p_M["v_y"], Fy_M/M_moon, 24*3600)
p_M["x"] += s(p_M['v_x'], Fx_M/M_moon, 24*3600)
p_M["y"] += s(p_M['v_y'], Fy_M/M_moon, 24*3600)
for i in range(0,len(t)):
xE += data_E[i]["x"]
yE += data_E[i]["y"]
xM += data_M[i]["x"]
yM += data_M[i]["y"]
print("\n Run time \n --- %d seconds ---" %(time.time()-start_time))
after run this code i tried to print data_E and data_M.
Then I can get data but there is no difference. All of the data is the same.
But when I printed data step by step, it totally different.
I have wrong data problem and increase distance problem. Please help me this problem..
The code exits near line 45, where you are trying to assign p_E by pulling the square root of a negative number on the right hand side (as you've moved the [0] coordinate of the Earth to negative values while shifting Earth and Moon into the coordinate system of their center of mass). In line 45, the value of F*rel_pE[0]/M_earth is negative. So the code never reaches the end of the program using python 2.7.14. That bug needs to be solved before trying to discuss any further aspects.
I've tried searching but none of the other questions seem to be like mine. I'm more or less experimenting with perspective projection and rotation in python, and have run into a snag. I'm sure my projection equations are accurate, as well as my rotation equations; however, when I run it, the rotation starts normal, but begins to swirl inwards until the vector is in the same position as the Z axis (the axis I am rotating over).
''' Imports '''
from tkinter import Tk, Canvas, TclError
from threading import Thread
from math import cos, sin, radians, ceil
from time import sleep
''' Points class '''
class pPoint:
def __init__(self, fPoint, wWC, wHC):
self.X = 0
self.Y = 0
self.Z = 0
self.xP = 0
self.yP = 0
self.fPoint = fPoint
self.wWC = wWC
self.wHC = wHC
def pProject(self):
self.xP = (self.fPoint * (self.X + self.wWC)) / (self.fPoint + self.Z)
self.yP = (self.fPoint * (self.Y + self.wHC)) / (self.fPoint + self.Z)
''' Main class '''
class Main:
def __init__(self):
''' Declarations '''
self.wWidth = 640
self.wHeight = 480
self.fPoint = 256
''' Generated declarations '''
self.wWC = self.wWidth / 2
self.wHC = self.wHeight / 2
''' Misc declarations '''
self.gWin = Tk()
self.vPoint = pPoint(self.fPoint, self.wWC, self.wHC)
self.vPoint.X = 50
self.vPoint.Y = 60
self.vPoint.Z = -25
self.vPoint.pProject()
self.ang = 0
def initWindow(self):
self.gWin.minsize(self.wWidth, self.wHeight)
self.gWin.maxsize(self.wWidth, self.wHeight)
''' Create canvas '''
self.gCan = Canvas(self.gWin, width = self.wWidth, height = self.wHeight, background = "black")
self.gCan.pack()
def setAxis(self):
''' Create axis points '''
self.pXax = pPoint(self.fPoint, self.wWC, self.wHC)
self.pXbx = pPoint(self.fPoint, self.wWC, self.wHC)
self.pYax = pPoint(self.fPoint, self.wWC, self.wHC)
self.pYbx = pPoint(self.fPoint, self.wWC, self.wHC)
self.pZax = pPoint(self.fPoint, self.wWC, self.wHC)
self.pZbx = pPoint(self.fPoint, self.wWC, self.wHC)
''' Set axis points '''
self.pXax.X = -(self.wWC)
self.pXax.Y = 0
self.pXax.Z = 1
self.pXbx.X = self.wWC
self.pXbx.Y = 0
self.pXbx.Z = 1
self.pYax.X = 0
self.pYax.Y = -(self.wHC)
self.pYax.Z = 1
self.pYbx.X = 0
self.pYbx.Y = self.wHC
self.pYbx.Z = 1
self.pZax.X = 0
self.pZax.Y = 0
self.pZax.Z = -(self.fPoint) / 2
self.pZbx.X = 0
self.pZbx.Y = 0
self.pZbx.Z = (self.fPoint * self.wWC) - self.fPoint
def projAxis(self):
''' Project the axis '''
self.pXax.pProject()
self.pXbx.pProject()
self.pYax.pProject()
self.pYbx.pProject()
self.pZax.pProject()
self.pZbx.pProject()
def drawAxis(self):
''' Draw the axis '''
self.gCan.create_line(self.pXax.xP, self.pXax.yP, self.pXbx.xP, self.pXbx.yP, fill = "white")
self.gCan.create_line(self.pYax.xP, self.pYax.yP, self.pYbx.xP, self.pYbx.yP, fill = "white")
self.gCan.create_line(self.pZax.xP, self.pZax.yP, self.pZbx.xP, self.pZbx.yP, fill = "white")
def prePaint(self):
self.vA = self.gCan.create_line(self.wWC, self.wHC, self.vPoint.xP, self.vPoint.yP, fill = "red")
def paintCanvas(self):
try:
while True:
self.ang += 1
if self.ang >= 361:
self.ang = 0
self.vPoint.X = (self.vPoint.X * cos(radians(self.ang))) - (self.vPoint.Y * sin(radians(self.ang)))
self.vPoint.Y = (self.vPoint.X * sin(radians(self.ang))) + (self.vPoint.Y * cos(radians(self.ang)))
self.vPoint.pProject()
self.gCan.coords(self.vA, self.wWC, self.wHC, self.vPoint.xP, self.vPoint.yP)
self.gWin.update_idletasks()
self.gWin.update()
sleep(0.1)
except TclError:
pass
mMain = Main()
mMain.initWindow()
mMain.setAxis()
mMain.projAxis()
mMain.drawAxis()
mMain.prePaint()
mMain.paintCanvas()
Thank you for any input :)
EDIT: Sorry, I just realized I forgot to put my question. I just want to know why it is gravitating inward, and not just rotating "normally"?
This section is wrong:
self.ang += 1
if self.ang >= 361:
self.ang = 0
self.vPoint.X = (self.vPoint.X * cos(radians(self.ang))
- self.vPoint.Y * sin(radians(self.ang)))
self.vPoint.Y = (self.vPoint.X * sin(radians(self.ang))
+ self.vPoint.Y * cos(radians(self.ang)))
self.vPoint.pProject()
For two reasons:
self.ang will take integers in the open range [0 - 360], which means the angle 360 (== 0) is repeated.
In each iteration, you rotate the point from the previous iteration by the angle. As a result, your first frame is at 1 degree, your second at 1+2 = 3, the third at 1 + 2 + 3... You should either be:
rotating the point from the previous iteration by a constant angle each time (1°). This suffers from the problem mentioned in my comment
rotating the initial point by the current angle of rotation each time
Not actualy related to your problem, but I strongly suggest you to use Numpy to perform geometric transformations, specially if it involves 3D points.
Below, I post a sample snippet, I hope it helps:
import numpy
from math import radians, cos, sin
## suppose you have a Nx3 cloudpoint (it might even be a single row of x,y,z coordinates)
cloudpoint = give_me_a_cloudpoint()
## this will be a rotation around Y azis:
yrot = radians(some_angle_in_degrees)
## let's create a rotation matrix using a numpy array
yrotmatrix = numpy.array([[cos(yrot), 0, -sin(yrot)],
[0, 1, 0],
[sin(yrot), 0, cos(yrot)]], dtype=float)
## apply the rotation via dot multiplication
rotatedcloud = numpy.dot(yrotmatrix, pointcloud.T).T # .T means transposition